Nous considérons une suite éventuellement fortement dépendante, avec un saut dans sa moyenne. Nous estimons le temps de rupture à partir des sommes partielles. La vitesse de convergence , typique pour des suites indépendantes, est aussi obtenu pour des suites de courte ou de longue mémoire.
We consider a (possibly) long-range dependent sequence with a shift in the mean. We estimate the location of the change-point using a cumulative sum estimator. The convergence rate typical of the independent case is also achieved for short-memory and long-memory sequences.
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@article{CRMATH_2005__341_12_765_0, author = {Ben Hariz, Samir and Wylie, Jonathan J.}, title = {Convergence rates for estimating a change-point with long-range dependent sequences}, journal = {Comptes Rendus. Math\'ematique}, pages = {765--768}, publisher = {Elsevier}, volume = {341}, number = {12}, year = {2005}, doi = {10.1016/j.crma.2005.10.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.10.003/} }
TY - JOUR AU - Ben Hariz, Samir AU - Wylie, Jonathan J. TI - Convergence rates for estimating a change-point with long-range dependent sequences JO - Comptes Rendus. Mathématique PY - 2005 SP - 765 EP - 768 VL - 341 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.10.003/ DO - 10.1016/j.crma.2005.10.003 LA - en ID - CRMATH_2005__341_12_765_0 ER -
%0 Journal Article %A Ben Hariz, Samir %A Wylie, Jonathan J. %T Convergence rates for estimating a change-point with long-range dependent sequences %J Comptes Rendus. Mathématique %D 2005 %P 765-768 %V 341 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.10.003/ %R 10.1016/j.crma.2005.10.003 %G en %F CRMATH_2005__341_12_765_0
Ben Hariz, Samir; Wylie, Jonathan J. Convergence rates for estimating a change-point with long-range dependent sequences. Comptes Rendus. Mathématique, Tome 341 (2005) no. 12, pp. 765-768. doi : 10.1016/j.crma.2005.10.003. http://archive.numdam.org/articles/10.1016/j.crma.2005.10.003/
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